Control and synchronizing nonlinear systems with delay based on a special matrix structure

This work presents a direct approach to design stabilizing controller for nonlinear systems with delay based on a special matrix structure and proves the validity of the approach according to Lyapunov-Krasovskii stable theorem and Linear Matrix Inequality-LMI. Control Lorenz system and synchronizing Rössler system with delay are taken as examples to explain the approach. Numerical simulations confirm the effectiveness of the approach proposed.